The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical claims. This assumption is unrealistic when, for example, we offer bets on remote digits of pi or when an agent faces a computationally intractable planning problem. Furthermore, the assumption of logical omniscience creates contradictions in cases where the environment can contain descriptions of the agent itself. Importantly, strategic interactions as studied in game theory are decision problems in which a rational agent is predicted by its environment (the other players). In this paper, we develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems (including ones like betting on digits of pi or games against other agents). The main contribution of this paper is to provide a sensible theory of rationality for such agents. Roughly, we require that a boundedly rational inductive agent tests each efficiently computable hypothesis infinitely often and follows those hypotheses that keep their promises of high rewards. We then prove that agents that are rational in this sense have other desirable properties. For example, they learn to value random and pseudo-random lotteries at their expected reward. Finally, we consider strategic interactions between different agents and prove a folk theorem for what strategies bounded rational inductive agents can converge to.

翻译：理性选择的主流理论假设逻辑全知性。也就是说，这些理论假设在面临决策问题时，智能体能够执行所有相关计算并确定所有相关逻辑/数学命题的真值。例如，当我们就π的远程数字打赌，或当智能体面临计算上难以处理的规划问题时，这一假设并不现实。此外，在环境可能包含智能体自身描述的情况下，逻辑全知性假设会引发矛盾。重要的是，博弈论中研究的策略互动正是这样一种决策问题：理性智能体被其环境（其他参与者）所预测。本文提出了一种不依赖逻辑全知性假设的理性决策理论。我们考虑反复面对决策问题（包括像π数字打赌或与其他智能体博弈等问题）的智能体。本文的主要贡献在于为这类智能体提供了一种合理的理性理论。大致而言，我们要求有界理性归纳型智能体无限频繁地测试每个高效可计算的假设，并遵循那些兑现高回报承诺的假设。随后我们证明，在此意义上理性的智能体具有其他理想性质。例如，它们能学会以期望奖励评估随机和伪随机彩票。最后，我们探讨不同智能体之间的策略互动，并证明了关于有界理性归纳型智能体可收敛到何种策略的民间定理。